Mayor Ed Lee – and his mustache – were MIA on Monday (Credit: The Chronicle)

Mayor Ed Lee usually has a good sense of humor when it comes to his famously bushy mustache. On Monday? Not so much. He skipped a City Hall event listed on his public calendar after a group of protesters announced they’d be outside picketing – and wearing fake mustaches.

Lee was due to speak alongside representatives of the city’s Department on the Status of Women, the Board of Supervisors and several local companies to promote San Francisco’s Gender Equality Challenge, a new effort to push private companies to advance gender equity in the workplace.

Companies with an office in San Francisco and at least 1,000 employees are eligible to enter the challenge in which they’ll promote a “model practice” like having an equal number of men and women in management positions or eliminating pay differences between men and women.

But a few hours before the event was due to start, female workers with Service Employees International Union Local 1021 announced their plans to station themselves outside the event wearing mustaches and carrying signs reading, “If I Were a Man, You Would Pay Me More.”

Susan Gard, chief of policy for the department, emphasized those classifications currently earn at least 20 percent more than their Bay Area counterparts — but that the wage cuts would affect only new hires. Wage increases would be offered for underpaid job classifications — current and future employees alike — including sheriff’s cadets and laboratory technicians.

The union counters that it’s more expensive to live in San Francisco than other parts of the Bay Area, and women who’ve fought to earn more here shouldn’t be penalized.

Christine Falvey, the mayor’s spokeswoman, appeared at the event in Lee’s stead and said the mayor was stuck in budget meetings. She said the mustachioed picketers had nothing to do with his absence.”Oh, no no no. He didn’t know this was happening,” she said of the protesters.

But Larry Bradshaw, a paramedic with the fire department and the vice president of SEIU 1021, wasn’t buying it.

“I don’t know how he would have threaded the needle” of promoting private gender equity, but not pay equity at City Hall, Bradshaw said.